Correlation Functions of Multisite Interaction Spin-S models on the Bethe-like Lattices

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for the correlation length and magnetic susceptibility are derived for spin-1/2 models. The singularity of the correlation length with critical index $\nu =1$ and the proportionality of magnetic susceptibility to correlation length in the second order phase transition region of spin-1/2 ferromagnetic models on the Bethe-like lattices are established analytically.Comment: 13 pages, In Press Int. J. Mod. Phys.

Energy Relaxation of Hot Dirac Fermions in Graphene

We develop a theory for the energy relaxation of hot Dirac fermions in graphene. We obtain a generic expression for the energy relaxation rate due to electron-phonon interaction and calculate the power loss due to both optical and acoustic phonon emission as a function of electron temperature $T_{\mathrm{e}}$ and density $n$. We find an intrinsic power loss weakly dependent on carrier density and non-vanishing at the Dirac point $n = 0$, originating from interband electron-optical phonon scattering by the intrinsic electrons in the graphene valence band. We obtain the total power loss per carrier $\sim 10^{-12} - 10^{-7} \mathrm{W}$ within the range of electron temperatures $\sim 20 - 1000 \mathrm{K}$. We find optical (acoustic) phonon emission to dominate the energy loss for $T_{\mathrm{e}} > (<) 200-300 \mathrm{K}$ in the density range $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.Comment: 5 page

Stochastic Lot Sizing for Shareholder Wealth Maximisation under Carbon Footprint Management

Fulltext in http://www.jiii.org/index.php?m=content&c=index&a=show&catid=41&id=141There is a growing consensus that human beings must cut greenhouse gas emissions to mitigate global warming and the resultant impacts on the environment. However, production optimisation has rarely taken this issue into consideration, often leading to environmentally unsustainable operation decisions. This paper presents a lot sizing batch optimisation model for a stochastic make-to-order production environment under the carbon emission trading mechanism—currently the most effective market-based carbon emission controlling system, with an aim to maximise the long-term sustainable interests of corporate owners, well-known as the shareholder wealth. To more closely reflect the real-world manufacturing environment, the proposed model adopts general distributions, instead of unrealistic theoretical assumptions, for random variables. We apply the model to investigate the impacts of the carbon emission trading mechanism on shareholder wealth, and test its hedging capability against a series of risk factors. The analytical results provide insights into production optimisation with carbon footprint management.International Conference on Industrial Engineering and Applications (ICIEA 2014), Sydney, Australia, 29-30 May 2014. In Journal of Industrial and Intelligent Information, 2015, v. 3 n. 1, p. 1-

A decomposition based algorithm for flexible flow shop scheduling with machine breakdown

Research on flow shop scheduling generally ignores uncertainties in real-world production because of the inherent difficulties of the problem. Scheduling problems with stochastic machine breakdown are difficult to solve optimally by a single approach. This paper considers makespan optimization of a flexible flow shop (FFS) scheduling problem with machine breakdown. It proposes a novel decomposition based approach (DBA) to decompose a problem into several sub-problems which can be solved more easily, while the neighbouring K-means clustering algorithm is employed to group the machines of an FFS into a few clusters. A back propagation network (BPN) is then adopted to assign either the shortest processing time (SPT) or the genetic algorithm (GA) to each cluster to solve the sub-problems. If two neighbouring clusters are allocated with the same approach, they are subsequently merged. After machine grouping and approach assignment, an overall schedule is generated by integrating the solutions to the sub-problems. Computation results reveal that the proposed approach is superior to SPT and GA alone for FFS scheduling with machine breakdown. © 2009 IEEE.published_or_final_versionThe IEEE International Conference on Computational Intelligence for Measurement Systems and Applications (CIMSA 2009), Hong Kong, 11-13 May 2009. In Proceedings of CIMSA, 2009, p. 134-13